Line Integrals Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Evaluate the line integral where is the curve given by and with    

(2) Evaluate the line integral where is the curve given by and with   

(3) Evaluate the line integral where is the curve given by with   

(4) Evaluate the line integral where is the quarter-circle from to

(5) Evaluate the line integral where is the curve defined by from to

(6) Evaluate the line integral where and is the boundary of the triangle with vertices and , transversed once clockwise, as viewed from above.

(7) A 5,000-lb satellite orbits the earth in a circular orbit 5,000 mi from the center of the earth. How much work is done as the satellite moves through one complete revolution?

(8) Suppose a particle with charge and mass moves with velocity under the influence of an electric field and a magnetic field Then the total force on the particle is called the Lorentz force. Use Newton's second law of motion, to show that



and then evaluate the line integral where is the trajectory of a particle traveling with constant speed.  

(9) Let and let and be the following two paths joining to

   and   

Show that Explain what this means?

(10) Evaluate the closed line integral where and is the boundary of the triangle with vertices and transversed once clockwise, as viewed from above.

(11) Evaluate the closed line integral where and is the boundary of the trapezoid with vertices and transversed once clockwise, as viewed from above.

(12) Find the work done by the force field on any object moving along the curve where is the path given by and for

(13)  Find the work done by the force field on any object moving along the curve where is the line segment from to

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